0580/42 February/March 2024 Question 10: Plotting Curves from a Table of Values

Question 1

Use the equation to calculate the missing y-values in the table for the given x-values.

Accepted Answer

x = −3: 2(−27) + 6(9) − 2.5 = −2.5 x = −0.5: 2(−0.125) + 6(0.25) − 2.5 = −1.25 x = 1: 2 + 6 − 2.5 = 5.5 Answer: | x | −3 | −0.5 | 1 |
| y | −2.5 | −1.25 | 5.5 |

Question 2

Plot the completed table points and draw the curve y = 2x³ + 6x² − 2.5 on the grid from x = −3 to 1.

Accepted Answer

Plot (−3, −2.5), (−2.5, 3.75), (−2, 5.5), (−1.5, 4.25), (−1, 1.5), (−0.5, −1.25), (0, −2.5), (0.5, −0.75), (1, 5.5) Join with a smooth curve: maximum at (−2, 5.5), minimum at (0, −2.5) Answer: Correct graph

Question 3

Sketch the curve, add a suitable straight line, and use its intersections to solve 2x³ + 6x² = 4.5.

Accepted Answer

2x³ + 6x² − 2.5 = 4.5 − 2.5, so draw the line y = 2 Read the x-values where the curve crosses y = 2 x ≈ −2.69, x ≈ −1.08, x ≈ 0.77 Answer: −2.75 to −2.65, −1.1 to −1.05, 0.75 to 0.85

Question 4

State the two values of k for which 2x³ + 6x² − 2.5 = k has exactly two solutions.

Accepted Answer

Exactly two solutions when the line y = k just touches a turning point Maximum at (−2, 5.5) and minimum at (0, −2.5) k = −2.5 or k = 5.5 Answer: −2.5, 5.5

0580/42 Feb/Mar 2024, Question 10: Plotting Curves from a Table of Values

The question, in short

Part (a) · 3 marks

Part (b) · 4 marks

Part (c) · 3 marks

Part (d) · 2 marks

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